The present invention is concerned with separation of small particles. More particularly, the invention is concerned with separation of small particles by use of a fluctuating potential acting on particles having a characteristic coefficient of friction.
Separation of small particles, especially colloidal particles, and in particular macromolecular biological particles in liquids, presents a technical challenge. Mechanical filtration is inadequate or ineffective and, if it is possible, is extremely slow. Mechanical filters are also likely to cause physical damage to proteins and other small particles (of the order of one to one thousand micrometers in major dimensions). The term "major dimension" is taken to mean the diameter of the smallest sphere that would contain the particles.
It is known that nonequilibrium fluctuations in time acting on a particle in an anisotropic periodic potential U(x) can cause transport of the particle in a medium. Thermal noise can complicate the situation and is sometimes necessary to get any flow at all. The study of such systems has been motivated in part by recent advances in the experimental study of motor proteins, i.e., proteins that convert the energy of ATP hydrolysis into motion along a biopolymer. These tiny engines may work by using the nonequilibrium fluctuations, brought about by the ATP turnover, to make a Brownian step in one direction more likely than in the opposite direction. This biasing of Brownian motion is an operating principle that is fundamentally different from that of macroscopic engines. Furthermore, nanotechnological devices have been constructed where the same principles are employed to drive microscopic particles.
In this application we cause a potential to fluctuate in such a way that the direction of the biasing depends on the coefficient of friction of the particle and thus we have a method for the separation of such particles. The setup is summarized by the following Langevin equation: ##EQU1## where .beta. is the coefficient of viscous friction, .xi.(t) is the function representing zero-average normalized white noise, and D controls the amplitude of this noise. The fluctuation-dissipation theorem D=kT/.beta. relates the coefficient of friction and the amplitude of thermal noise. The functions f(t) and g(t) describe the "nonthermal" additive and multiplicative noise, respectively. When g(t) does not vary in time and f(t)=0 no transport can occur. Transport occurring with f(t)=0 and constant g(t) means that thermal fluctuations are converted into work and implies a violation of the second law of thermodynamics. A great many investigations have focused on additive fluctuations or oscillations. In our method we focus on multiplicative noise, i.e., a g(t) that varies in time while f(t)=0, which means that the periodic potential changes shape but no net macroscopic force every occurs. The study of multiplicative noise has already led to the construction of a device to drive and possibly separate small particles or macromolecules. Multiplicative noise is also more likely to be the operating principle for motor proteins. The binding of ATP, the subsequent hydrolysis, and the release of ADP do not cause a macroscopic force along a biopolymer, but simply change the distribution of charges in the motor protein and thus the energy profile that the motor protein "feels" on the periodic biopolymer. The fluctuations of this profile can account for the observed speeds and stopping forces of real motors.
The models for which fluctuation-induced flow has been studied have generally been as simple as possible. A piecewise-linear potential with two pieces per period and a two-state additive or multiplicative Markovian fluctuation allows for analytic evaluation and it can, furthermore, be understood how and why flux occurs and how and why it changes when parameter values are changed. But when only slight complications are added the behavior of the system can become surprisingly rich and flux can actually change its direction more than once when a certain parameter is varied. In the prior art a two-piece piecewise-linear potential has been examined, and this examination showed how in the fast noise limit of an added fluctuation the direction of the induced flow depends on a characteristic of the noise. In a similar system with a three-state fluctuating force the many flux reversals were explained as noise characteristics were varied. Other prior art investigated a three-piece piecewise-linear potential. When transition rates between such a potential and a flat potential are changed, a reversal of flow occurs. While the prior art methods have observed a variety of interesting characteristics of particle flux, there has been no demonstration of the ability to efficiently separate different particles sizes.
It is therefore an object of the invention to provide an improved method and system for separating small particles.
It is another object of the invention to provide a novel method and system for applying a fluctuating potential to separate smaller colloidal particles from larger colloidal particles.
It is a further object of the invention to provide a method and system for applying a motor force to a molecule that is attached to a biopolymer.
These and other objects of the invention will become apparent by reference to the description of the invention.